In this case, the individual statements are plainly nonsensical if we are using
the usual connotations of the words. Yet both instances of the syllogism have the
same structure and it is the structure which makes this syllogism valid. It is
simply not possible to find an instance of As, Bs and Cs with this structure where
the premises are true but the conclusion is false. This is what makes a valid
argument useful.
A valid argument
A variety of syllogisms are possible if we vary the quantifiers such as ‘All’,
‘Some’ and ‘No’ (as in No As are Bs). For example, another might be
Is this a valid argument? Does it apply to all cases of As, Bs and Cs, or is there
a counterexample lurking, an instance where the premises are true but the
conclusion false? What about making A spaniels, B brown objects, and C tables?
Is the following instance convincing?
Our counterexample shows that this syllogism is not valid. There were so
many different types of syllogism that medieval scholars invented mnemonics to
help remember them. Our first example was known as BARBARA because it
contains three uses of ‘All’. These methods of analysing arguments lasted for